内容提要 本书是一部统计学方面的专著,每章首先介绍理论,其次使用资源R包将其应用于说明性示例中,列出一些练习,最后以参考文献结尾。本书共分为4章,介绍了网格数据点、单位面积数据点、映射点模式数据、高斯随机域、平稳性概念、协方差函数的构造、简单克里格方法、半方差函数、贝叶斯估计、离散随机域、高斯自回归模型、马尔可夫随机域、欧几里得空间上的点过程、泊松过程、有限点过程、分层建模等内容。本书适合数学、工程学、统计学研究生参考阅读。 目录 Preface AuthorCHAPTER 1 Introductio1.1 GRIDDED DATA1.2 AREAL UNIT DATA1.3 MAPPED POINT PATTERN DATA1.4 PLAN OF THE BOOKCHAPTER 2 Random field modelling and interpolatio2.1 RANDOM FIELDS2.2 GAUSSIAN RANDOM FIELDS2.3 STATIONARITY CONCEPTS2.4 CONSTRUCTION OF COVARIANCE FUNCTIONS2.5 PROOF OF BOCHNER'S THEOREM2.6 THE SEMI-VARIOGRAM2.7 SIMPLEKRIGING2.8 BAYES ESTIMATOR2.9 ORDINARY KRIGING2.10 UNIVERSAL KRIGING2.11 WORKED EXAMPLES WITH R2.12 EXERCISES2.13 POINTERS TO THE LITERATURECHAPTER 3 Models and inference for areal unit data3.1 DISCRETE RANDOM FIELDS etnefno3.2 GAUSSIAN AUTOREGRESSION MODELS3.3 GIBBS STATES3.4 MARKOV RANDOM FIELDS3.5 INFERENCE FOR AREAL UNIT MODELS3.6 MARKOV CHAIN MONTE CARLO SIMULATION3.7 HIERARCHICAL MODELLING3.7.1 Image segmentatio3.7.2 Disease mapping3.7.3 Synthesis3.8 WORKED EXAMPLES WITH R3.9 EXERCISES3.10 POINTERS TO THE LITERATURECHAPTER 4 Spatial point processes4.1 POINT PROCESSES ON EUCLIDEAN SPACES4.2 THE POISSON PROCESS4.3 MOMENT MEASURES4.4 STATIONARITY CONCEPTS AND PRODUCT DENSITIES4.5 FINITE POINT PROCESSES4.6 THE PAPANGELOU CONDITIONAL INTENSITY4.7 MARKOV POINT PROCESSES4.8 LIKELIHOOD INFERENCE FOR POISSON PROCESSES4.9 INFERENCE FOR FINITE POINT PROCESSES4.10 COX PROCESSES4.10.1 Cluster processes4.10.2 Log-Gaussian Cox processes4.10.3 Minimum contrast estimatio4.11 HIERARCHICAL MODELLING4.12 WORKED EXAMPLES WITH R4.13 EXERCISES4.14 POINTERS TO THE LITERATUREAppendix:Solutions to theoretical exercisesIndex编辑手记 作者介绍 M.N.M.范·利舒特,荷兰人,荷兰阿姆斯特丹数学与计算机科学中心(CWI)的高级研究员,并在特温特大学担任空间随机学教授。 序言
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